Parsonage is a generic term for the Anglican clergyman's residence -- it would have been a vicarage or a rectory depending on whether the incumbent was a vicar or a rector, which depended in turn on whether the parish's greater tithes belonged to the patron (vicar) or to the incumbent (rector).

I've stayed in a few and seen descriptions of a lot more English former parsonages that have been converted to a bed and breakfast or small country hotel. The Anglican parson was a gentleman and would have expected to be housed in solid comfort. Six bedrooms or so (plus servants' rooms) seems about the right size range to allow for children and visitors.